Introduction

As a human response to the perception of a cognitively chaotic situation, WH-questions (when, where, which, how, what, who/whose, why/wherefore) might be considered to lend themselves to analysis with the tools of catastrophe theory as developed by Rene Thom and others. Thom had developed differential topology into a general theory of form and change of form as a mathematical way of addressing the work on morphogenesis done by C.H. Waddington in the 1950's. Thom's Classification Theorem culminates a long line of work in singularity theory. The term "catastrophe theory" was suggested by C. Zeeman (1977) to unify singularity theory, bifurcation theory and their applications. The crucial theorems rigorously establishing Thom's conjecture were proven by Bernard Malgrange (1966) and John N. Mather (1968). Its essential concern is change and discontinuity in systems (cf Robert Magnus, Mathematical models and catastrophes). WH-questions may be considered as triggered and formulated in response to discontinuity -- when habitual adaptive responses to change are inadequate.

It is possible therefore that the set of WH-questions may in some way be mapped onto elementary catastrophes. This is partially suggested by mathematical techniques of conformal mapping where, for example, the "cognitive flow field" around one known shape (as with an elementary catastrophe) might be mapped onto the flow field around a particular WH-question -- preserving the "angles". Conformal mapping notably makes use of complex variables as combinations of real and imaginary numbers. [applet]

Whilst the purpose here is to highlight the role of why-questions in the set of WH-questions in the light of catastrophe theory, there is a certain irony to the following description of Thom's own focus by Christer Persson (Elementary catastrophe theory: an introduction):

In science two main lines of questioning compete or co-operate; one asking "How?", the other asking "Why?". In biology Thom had an irritating tendency to counter each answer to a "Why?"-question with cascades of "How?"-questions, the intent being to demonstrate the inadequateness or provisional character of "guiding thought" in biology. When answered: "Because messenger-RNA duplicates information from the DNA spiral and turns to ribosomes, where proteins are synthesized...", he promptly asked: When? How does it know when? How does it switch from one state to another? Following what roads? Where is the map?

Given Rene Thom's interest in semantics and linguistics, the discontinuity introduced into discourse by a question, and his predisposition to question the assumptions of others, it might be asked whether he endeavoured -- perhaps self-reflexively -- to relate elementary catastrophes to WH-questions in some way that is not evident in the published literature.